If a Ferrari, with an initial velocity of 10m/s, accelerates at at rate of 50m/s/s for 3 seconds, what will its final velocity be?
The Correct Answer and Explanation is:
To determine the final velocity of the Ferrari, we can use the basic kinematic equation for velocity:
[
v_f = v_i + a \cdot t
]
Where:
- ( v_f ) is the final velocity,
- ( v_i ) is the initial velocity,
- ( a ) is the acceleration, and
- ( t ) is the time.
Step-by-Step Calculation:
Given:
- Initial velocity (( v_i )) = 10 m/s,
- Acceleration (( a )) = 50 m/s²,
- Time (( t )) = 3 seconds.
Substitute the given values into the equation:
[
v_f = 10 \, \text{m/s} + (50 \, \text{m/s}^2 \cdot 3 \, \text{seconds})
]
First, calculate the acceleration term:
[
50 \, \text{m/s}^2 \cdot 3 \, \text{seconds} = 150 \, \text{m/s}
]
Now, substitute this value back into the equation:
[
v_f = 10 \, \text{m/s} + 150 \, \text{m/s} = 160 \, \text{m/s}
]
Final Answer:
The final velocity of the Ferrari will be 160 m/s.
Explanation:
This problem involves basic kinematics, which is the study of motion without considering the forces that cause it. In this case, we are concerned with the motion of the Ferrari under constant acceleration.
The Ferrari starts at an initial velocity of 10 m/s, which means that right from the start, it’s moving at 10 meters per second. The acceleration tells us that for every second that passes, the Ferrari’s speed increases by 50 meters per second.
Over the 3-second period, the car’s speed increases by ( 50 \, \text{m/s}^2 \times 3 \, \text{seconds} = 150 \, \text{m/s} ), so its final velocity after 3 seconds is the sum of its initial velocity (10 m/s) and the change in velocity (150 m/s), which gives a final velocity of 160 m/s.
This result illustrates how velocity increases under constant acceleration, and it shows the power of the Ferrari to rapidly speed up in a short amount of time.